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Thick Cylinders.

399

Example 7.—Find the bursting resistance of a cast-iron pipe | in.
thick and 10 ins. diameter.    (Eng. Exam., 1887.)
/tonsr = // (there being no seam)

j0t°«s = •£- =-75 ton = 1680 Ibs. per sq. in.

Second Case, Thick Cylinders. — If cylinder thickness be small
in comparison to diameter, the stress at the inner surface is
practically the same as at the outside. But this is by no means the
case with very thick cylinders. Then the following formula must
be applied, devised by Lam<£ :

R"     D      V/t +/Tonl

"~                       •

and the stress varies throughout the thickness, the hoop tension
ft being found at any intermediate radius i by the following
formula:                                    ;*ton V2 <Y2 + R2^

A m tons =^2:;7^

Example 8.— A cast-iron hydraulic cylinder is 6" internal diameter,
and loaded with i ton per sq. in. pressure. Find (i) the thickness,
and (2) construct a curve shewing the hoop tension throughout the
thickness.

•  R"=9     and_£=6"
r      V-/tOM           i'25-r                         y    - —

The section of the cylinder is shewn at Fig. 352, and the ordinates

at afrcdefg shew the hoop tension at the various rings, found as

follows:-                           1x9(814-9)

at a, yk= -~r )a7~~( « *"*$ tons
9    (oi-g)

Similarly  at £, /&**  76 ton,   at c«  '53 ton,         at ^= '406 ton,

at/«*283 ton,   and at^*— "25 ton,*